Difference between revisions of "1963 TMTA High School Algebra I Contest Problem 35"

Latest revision as of 12:18, 2 February 2021

Combine and simplify $\frac{2}{6-3x}+\frac{5}{x-2}-\frac{3}{4-2x}$

$\text{(A)} \quad \frac{-35}{6(x-2)} \quad \text{(B)} \quad \frac{-35}{6(2-x)} \quad \text{(C)} \quad \frac{35}{6(2-x)}$

$\text{(D)} \quad \frac{6}{2-x} \quad \text{(E)} \quad \frac{6}{x-2}$

The common denominator is $(2)(3)(x-2).$ $\frac{2}{6-3x}+\frac{5}{x-2}-\frac{3}{4-2x}=\frac{(-2)+6(5)-(-3)}{(2)(3)(x-2)}=\frac{35}{6x-12}$

The answer is $\boxed{\text{(B)}}.$

@@ Line 8: / Line 8: @@
 == Solution ==
 The common denominator is <math>(2)(3)(x-2).</math>
-<cmath>\frac{2}{6-3x}+\frac{5}{x-2}-\frac{3}{4-2x}=\frac{e}{(2)(3)(x-2)</cmath>
+<cmath>\frac{2}{6-3x}+\frac{5}{x-2}-\frac{3}{4-2x}=\frac{(-2)+6(5)-(-3)}{(2)(3)(x-2)}=\frac{35}{6x-12}</cmath>
+The answer is <math>\boxed{\text{(B)}}.</math>
 == See Also ==

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 34	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 36